1. Lesson 4 Circuits and Resistance

2. Class 9
Today we will:
learn about current, voltage, and power in circuits.
learn about resistance of materials and how resistance depends on geometry and temperature.
introduce Ohm’s law.

3. Current, Voltage, and Power in Simple Circuits

4. Current
Benjamin Franklin didn’t know if current was caused by positive charges moving or negative charges moving, so he took a guess… and got it wrong.
Current
Current was defined as the direction positive charge in a wire would travel.

5. Current
In reality, negative charges are moving in the opposite direction to the current.
Current
However, we usually ignore that and talk about “positive charge carriers” in a wire that move in the direction of the current.

6. Current
Current is the charge that moves past a point in the wire per unit time.

7. Current Units of current are amperes or amps.
Car batteries deliver several hundred amperes.
Most electronic circuits run on a few mA.

8. Voltage Voltage is electric potential in circuits.
Voltage is provided by batteries or generators.
A battery pushes electrons out the negative terminal and sucks electrons into the positive terminal.

9. Voltage
If we attach a wire to the positive terminal, a few go into the battery, leaving a positive charge on the surface of the wire.
The electrons stop moving when the surface charge on the wire pulls the electrons in the wire with the same force as the positive charge on the battery. +

10. Circuits
If we connect a wire from the positive to the negative terminal of the battery, current will continue to flow through the circuit.
– – – – – +
– – – – +

11. Circuits
Charge remains on the surface of the wire. The surface charge is positive near the positive terninal and negative near the negative terminal.
The charge density is greatest near the terminals of the battery.
Current flows uniformly through the entire cross-section of the wire.
– – – – – +
– – – – +

12. Circuits
A 10V battery gives 10eV of energy to each electron that passes through it.
Collisions with atoms in the wire cause each electron to lose 10eV of energy every time it goes around the circuit.
– – – – – +
– – – – +

13. Ground The ground acts like a huge conductor.
Current can flow into the ground or out of the ground without any limits.
The two circuits below are equivalent. + +

14. Circuits Definitions:
An open circuit is one where there is an open switch or a broken wire so that no current flows.
A closed circuit is one in which there is a continuous path for current to flow from positive to negative.
A short circuit is one where there is an unintentional current path to ground. Currents, sometimes large, flow where they should not, leading to shock and fire hazards.

15. Circuits What good does flowing charge do? Produces heat, light.
Produces magnetic fields – used in motors, vibrators, etc. to give mechanical power.
Produces electromagnetic radiation – radio waves for communication.
Electronics: amplification, logic, light detection, radiation detection, cathode-ray tubes, etc.

16. Power
Each time an electron goes through a battery, it gains energy. The total energy gained per second is:
Power provided by the battery!
P=iV

17. Where does the energy go?
Electrons collide with other electrons in atoms and quickly reach terminal velocity – so they don’t keep gaining kinetic energy.

18. Where does the energy go?
P=iV
In a wire, it goes to heat.
In other devices it can go to light, mechanical energy, energy of radiation fields, etc.

19. Resistance

20. Resistance in a Wire
Definition:
In general R is a function of I, and V.
For many materials R is nearly a constant.
When R is a constant, we call the material “ohmic.”

21. Resistors Devices to increase the resistance in part of a circuit.
Made of graphite chunks, wire wound around a core, etc.
Used to
Produce heat or light
Adjust current flow and voltages in circuits.

22. Resistors
Even if we don’t want the resistance, we often need to account for resistance in cables, electronic devices, etc.

23. Ohm’s Law We assume resistors have constant V.
Resistance has units of ohms, written as an upper case omega.
Typical resistances range from a few ohms to several megohms.

24. Graphite Resistors Resistance is color coded. R=5600 Ω (+/-10%) 1 2 31 2 3 4 5 6 7 8 9 5%
10%
20% 5 6 2
10%
second digit
# of zeros
tolerance
first digit
R=5600 Ω (+/-10%)

25. What Affects Resistance?
Material
Length
Cross-sectional area
Temperature

26. Resistance and Geometry
One block has V, I, R.

27. Resistance and Geometry
Take two blocks with I going through each.
Voltage is Current is
Resistance is

28. Resistance and Geometry
Take two blocks with I going through each.
Voltage is Current is
Resistance is

29. Resistance and Resistivity
ρ is the resistivity. It depends on the material from which the resistor is made. The units of resistivity are Ωm.
σ = 1/ ρ is the conductivity
Head into series and parallel….

30. Resistance and Temperature
We assume that resistance varies linearly with temperature.

31. Resistance and Temperature
If T = T0, then R =R0.

32. Resistance and Temperature
α is the temperature coefficient of resistivity (resistance).
α is usually positive.
α is negative for graphite.

33. Class 10
Today we will:
learn how to determine if two resistors are in series or parallel.
find out how resistors combine when connected in series and parallel.
work examples of series-parallel reduction to find current, voltage and power in resistance networks.

34. Resistors in Series Have the Same Current
Take two resistors with I going through each.
Voltage is Current is
Resistance is

35. Resistors in Series

36. Resistors in Parallel Have the Same Voltage
Take two blocks with I going through each.
Voltage is Current is
Resistance is

37. Resistors in Parallel Have the Same Voltage

38. A Test for Resistors in Series
Look at the wire connecting the two resistors. Is there any junction between the resistors?
The resistors are connected in series.
The resistors are NOT connected in series. no
yes

39. A Test for Resistors in Parallel
Look at the wire connecting one end of the first resistor to one end of the second resistor. Is there a circuit element (a junction is OK and usually there are junctions) along this wire?
yes no
The resistors are NOT connected in parallel.
Look at the wire connecting the other end of the first resistor to the other end of the second resistor. Is there a circuit element along this wire? no
yes
The resistors are connected n parallel.
The resistors are NOT connected n parallel.

40. Series-Parallel Quiz Answer the following six questions to see if you understand what series and parallel mean.

41. Resistors A and B are in
series
parallel
neither

42. Resistors A and B are in
series
parallel
neither

43. Resistors A and B are in
series
parallel
neither

44. Resistors A and B are in
series
parallel
neither

45. Resistors A and B are in
series
parallel
neither

46. Resistors A and B are in
series
parallel
neither

47. Quiz Answers 1. series 2. neither 3. neither 4. parallel 5. series 6
Quiz Answers 1. series 2. neither 3. neither 4. parallel 5. series 6. parallel

48. Series- Parallel Reduction
Find a combination in series or parallel.
Combine resistors into a single equivalent resistor.
Repeat until there is only one resistor.
The voltage across the resistor is the same as the voltage across the battery.

49. Series- Parallel Reduction
Find V, I, R, P for the last step.
Bootstrap your way back to the beginning, diagram by diagram.
What if there are resistors that aren’t in series or parallel?
--- You’ll need to use Kirchhoff’s Laws which we’ll learn later.

50. Now we’ll work some examples…

51. Find all the currents, voltages, and powers

55. 2A
24V,2A

56. 2A 2A 2A

57. 2A, 4V 2A
2A, 20V

58. 4V 4V 2A
2A, 20V

59. 4V, 2/3 A
4V, 4/3 A 2A
2A, 20V

60. 2/3 A
2/3 A
4V, 4/3 A 2A 2A 2A

61. 2/3 A, 8/3 V
2/3 A, 4/3 V
4V, 4/3 A 2A
2A, 4V
2A, 16V

62. 16/9 W
8/9 W
2/3 A, 8/3 V
2/3 A, 4/3 V
4V, 4/3 A
16/3 W 2A
2A, 4V
48 W
2A, 16V
8 W
32 W

63. Using Meters
Ammeters measure current. they must be paced in series with other circuit elements so current flows through them. Ammeters should have very small voltage.
Voltmeters measure voltage. To measure the voltage between two points, you connect the two leads of the meter to those points. Therefore voltmeters are placed in parallel. Voltmeters should have large voltage.

64. Real Batteries
Real batteries have internal resistance. When they are placed in a circuit we can represent them as a resistor in series with an ideal battery.
There’s a voltage drop across the internal resistance.
This means that the full voltage of the ideal battery isn’t available to the circuit.

65. Class 11 Today we will: discuss Kirchhoff’s loop and node equations.
learn how to determine the number of loop and the number of node equations we will need.
write Kirchhoff’s equations for a sample circuit.

66. Kirchhoff’s Junction Rule
Current into a junction equals current out of a junction.
Comes from conservation of charge.

67. Kirchhoff’s Junction Rule
It’s like water in pipes – the water flowing into a junction must flow out again.

68. Kirchhoff’s Loop Rule
The net change in voltage around a closed loop is zero.
Comes from Conservation of energy

69. Kirchhoff’s Loop Rule
It’s like moving a ball around any closed path, the change in gravitational potential energy is zero.

70. Applying Kirchhoff’s Laws
This is a “turn the crank” approach – but it works well.

71. Mark each junction. A B D C

72. Here there are 6 currents.
2. Label all currents – between each pair of junctions. Choose a direction – it doesn’t have to be right!
Here there are 6 currents. A I1 I3 B I6 D I4 I5 I2 C

73. Here there are 4 junctions, so there are 3 junction equations.
3. Number of junction equations: If there are N junctions, there are N-1 junction equations.
Here there are 4 junctions, so there are 3 junction equations. A I1 I3 B I6 D I4 I5 I2 C

74. 4. Write the junction equations: Current in = Current out.B I6 D I4 I5 I2 C

75. Here: 6-3=3, so we need 3 loops.
5. Number of loop equations: Number of currents – Number of junction equations.
Here: 6-3=3, so we need 3 loops. A I1 I3 B I6 D I4 I5 I2 C

76. 6. At least one loop must cover every circuit element.1 2 B I6 D I4 I5 3 I2 C

77. 7. Put a plus or minus on every resistor (side current goes in is +) and battery (+ is positive terminal). A I1 + + I3 + 1 + 2 B I6 D + + I4 I5 3 I2 + + C

78. 8. Write the loop equations.+ + I3 + 1 + 2 B I6 D + + I4 I5 3 I2 + + C

79. 8. Write the loop equations.
When you go around the loop, ignore the current
arrows! Follow the loop in the direction of the loop
arrow! A I1 + + I3 + 1 + 2 B I6 D + + I4 I5 3 I2 + + C

80. 8. Solve the system of equations using your favorite method
8. Solve the system of equations using your favorite method. I’ll usually just ask for the equations.